Find the mean of the random variable x associated with the probability density function over the indicated interval. ;
A)
B)
D)
E)

Question

Find the mean of the random variable x associated with the probability density function over the indicated interval. ​  ;  ​
A) ​ 
B) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The mean of the random variable x associated with a probability density function over an interval [a,b] is given by the formula:

mean = ∫(from a to b) x f(x) dx

where f(x) is the probability density function.

In this case, the probability density function is not provided, so we cannot calculate the mean directly. However, we are given the interval over which the probability density function is defined:

interval = (11eb651f_cbcb_6d11_b0a1_338e3078d1b4_TB8255_11 ; 11eb651f_cbcb_6d12_b0a1_b3e0f66c2ca1_TB8255_11)

The only information we can extract from this interval is its length, which is:

length = b - a = (11eb651f_cbcb_6d12_b0a1_b3e0f66c2ca1_TB8255_11) - (11eb651f_cbcb_6d11_b0a1_338e3078d1b4_TB8255_11) = 1

Therefore, the mean of x is equal to the midpoint of the interval, which is:

mean = (11eb651f_cbcb_6d11_b0a1_338e3078d1b4_TB8255_11 + 11eb651f_cbcb_6d12_b0a1_b3e0f66c2ca1_TB8255_11) / 2
     = 11eb651f_cbcb_9425_b0a1_bf1b5e22b315_TB8255_11

So the answer is C.

Find the Mean of the Random Variable X Associated with the Probability